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ehrenfest
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Homework Statement
Can someone define the phrase "quantize a string" as seen at
http://books.google.com/books?id=Xm...gAQ&sig=Eqnkxjj7B9gc4-nig1fgUkk7AqQ#PPA206,M1
?
Quantizing a theory consists in two steps. One, the dynamic variables are turned into Hilbert space operators, and two the commutations relations among those operators are found.ehrenfest said:Can someone define the phrase "quantize a string"?
Zwiebach said:As a first step in defining a quantum theory of the light-cone relativistic string, we must give the list of Shrodinger operators.
And then the deed is done.Zwiebach said:Now we set up the commutation relations
String theory is a theoretical framework in physics that attempts to reconcile general relativity and quantum mechanics by postulating that the fundamental building blocks of the universe are not particles, but tiny, vibrating strings.
Quantization in string theory refers to the process of translating the continuous vibrations of a string into discrete energy levels, similar to the quantization of energy levels in atoms. This is necessary in order to mathematically describe the behavior of strings in a consistent way.
The quantization of strings allows for the prediction of physical phenomena that cannot be explained by classical physics, such as the existence of extra dimensions and the behavior of black holes. It also helps to reconcile the discrepancies between general relativity and quantum mechanics.
In string theory, the quantization of a string is achieved by considering the string's energy and momentum as operators that act on a state known as the string state. The resulting equation, known as the string wave equation, describes the behavior of the string as it vibrates in different energy states.
One of the main challenges in quantizing a string is the fact that the theory requires a higher-dimensional space, which can be difficult to visualize and work with mathematically. Another challenge is the lack of experimental evidence for string theory, making it difficult to test and validate its predictions.